Homology of artinian and mini-max modules, II

Bethany Kubik, Micah Leamer, Sean Sather-Wagstaff

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let R be a commutative ring, and let L and L' be R-modules. We investigate finiteness conditions (e.g., noetherian, artinian, mini-max, Matlis reflexive) of the modules ExtRi(L,L') and ToriR(L,L') when L and L' satisfy combinations of these finiteness conditions. For instance, if R is noetherian, then given R-modules M and M' such that M is Matlis reflexive and M' is mini-max (e.g., noetherian or artinian), we prove that ExtRi(M,M'), ExtRi(M',M), and ToriR(M,M') are Matlis reflexive over R for all i≥0 and that ExtRi(M,M')∨≅ToriR(M,M'∨) and ExtRi(M',M)∨≅ToriR(M',M∨).

Original languageEnglish (US)
Pages (from-to)229-272
Number of pages44
JournalJournal of Algebra
Volume403
DOIs
StatePublished - Feb 1 2014

Keywords

  • Artinian
  • Bass number
  • Betti number
  • Ext
  • Hom
  • Matlis duality
  • Mini-max
  • Noetherian
  • Primary
  • Secondary
  • Tensor product
  • Tor

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